The speed of a boat in still water is 6, km/h | vedclass

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(B) Let the speed of the boat in still water be $u = 6\, km/h$ and the speed of the stream be $v\, km/h$.The speed of the boat upstream is $(u - v) =

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(B) Let the speed of the boat in still water be $u = 6\, km/h$ and the speed of the stream be $v\, km/h$.The speed of the boat upstream is $(u - v) = (6 - v)\, km/h$.The speed of the boat downstream is $(u + v) = (6 + v)\, km/h$.Let the distance be $d$. The time taken to row upstream is $T_{up} = \frac{d}{6 - v}$ and the time taken to row downstream is $T_{down} = \frac{d}{6 + v}$.According to the problem,the time taken to row upstream is twice the time taken to row downstream:$T_{up} = 2 	imes T_{down}$$\frac{d}{6 - v} = 2 	imes \frac{d}{6 + v}$Canceling $d$ from both sides:$\frac{1}{6 - v} = \frac{2}{6 + v}$$6 + v = 2(6 - v)$$6 + v = 12 - 2v$$3v = 6$$v = 2\, km/h$.Thus,the rate of the stream is $2\, km/h$.

The speed of a boat in still water is $6\, km/h$. It takes the boat twice as long to row up as to row down the river. Find the rate of the stream (in $km/h$).

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